In this work, the effect of fluid flow on the morphology of the weld pool and the welding properties during Tungsten Inert Gas (TIG) process using 304L stainless steel is investigated. In the first part, a computation code under Fortran was elaborated to solve the equations resulting from the finite difference discretization of the heat equation, taking into account the liquid-solid phase change with the associated boundary conditions. In order to solve the Navier-Stokes equations expressed in the stream-vorticity formulation, a mathematical model was developed to study the effect of the melted liquid movement on the weld joint. The evolution of the fraction volume of the liquid and the thermal fields promoted the determination of the molten zone (MZ) and the Heat Affected Zone (HAT)dimensions, which seems to be in good agreement with literature.